A New Encoding and Implementation of Not Necessarily Closed Convex Polyhedra (TR)

[Page last updated on "January 13, 2005, 15:31:42".]

Roberto Bagnara, Patricia M. Hill, and Enea Zaffanella

Abstract

Convex polyhedra, commonly employed for the analysis and verification
of both hardware and software, may be defined either by a finite set
of linear inequality constraints or by finite sets of generating
points and rays of the polyhedron. Although most
implementations of the polyhedral operations assume that the polyhedra
are topologically closed (i.e., all the constraints defining them are
non-strict), several analyzers and verifiers need to compute on a domain of
convex polyhedra that are not necessarily closed (NNC). The usual
approach to implementing NNC polyhedra is to embed them into closed
polyhedra in a vector space having one extra dimension and
reuse the tools and techniques already available for closed polyhedra.
Previously, this embedding has been designed so that a constant number
of constraints and a linear number of generators have to be added to
the original NNC specification of the polyhedron. In this paper we
explore an alternative approach: while still using an extra dimension
to represent the NNC polyhedron by a closed polyhedron, the new
embedding adds a linear number of constraints and a constant number of
generators.
As far as the issue of providing a non-redundant description of the
NNC polyhedron is concerned, we generalize the results established
in a previous paper so that they apply to both encodings.